Arnold's conjecture and symplectic reduction

DOI10.1016/0393-0440(96)89538-6zbMath0878.58025OpenAlexW2057112782WikidataQ123224944 ScholiaQ123224944MaRDI QIDQ679524

C. Martínez Ontalba, Alberto Ibort

Publication date: 8 January 1998

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0393-0440(96)89538-6

zbMATH Keywords

critical pointsArnold's conjecturesymplectic reduction

Mathematics Subject Classification ID

Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Pseudodifferential and Fourier integral operators on manifolds (58J40) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)

Cites Work

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• \(R^{2n}\) is a universal symplectic manifold for reduction
• A symplectic fixed point theorem for \({\mathbb{C}}P^ n\)
• A symplectic fixed point theorem on \(T^{2n}\times {\mathbb{C}}P^ k\)
• A universal phase space for particles in Yang-Mills fields
• Symplectic fixed points, the Calabi invariant and Novikov homology. [Appendix C in collaboration with Lê Tu Quôc Thang]
• Symplectic fixed points and holomorphic spheres
• On the Arnold conjecture for weakly monotone symplectic manifolds
• A symplectic fixed point theorem for complex projective spaces

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